The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps

Aas, Erik and Ayyer, Arvind and Linusson, Svante and Potka, Samu (2019) The exact phase diagram for a semipermeable TASEP with nonlocal boundary jumps. In: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 52 (35).

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Abstract

We consider a finite one-dimensional totally asymmetric simple exclusion process with four types of particles, { 1, 0, (1)over-bar, *}, in contact with reservoirs. Particles of species 0 can neither enter nor exit the lattice, and those of species * are constrained to lie at the first and last site. Particles of species 1 enter from the left reservoir into either the first or second site, move rightwards, and leave from either the last or penultimate site. Conversely, particles of species 1 enter from the right reservoir into either the last or penultimate site, move leftwards, and leave from either the first or last site. This dynamics is motivated by a natural random walk on the Weyl group of type D. We compute the exact nonequilibrium steady state distribution using a matrix ansatz building on earlier work of Arita. We then give explicit formulas for the nonequilibrium partition function as well as densities and currents of all species in the steady state, and derive the phase diagram.

Item Type:	Journal Article
Publication:	JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Publisher:	IOP PUBLISHING LTD
Additional Information:	copyright for this article belongs to IOP PUBLISHING LTD
Keywords:	exclusion process; two-species; nonlocal boundary jumps; phase diagram; current; fat shock
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	05 Sep 2019 10:12
Last Modified:	05 Sep 2019 10:12
URI:	http://eprints.iisc.ac.in/id/eprint/63445

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